Distribution of Eigenvalues in Non-Hermitian Anderson Models
- 30 March 1998
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 80 (13) , 2897-2900
- https://doi.org/10.1103/physrevlett.80.2897
Abstract
We develop a theory which describes the behavior of eigenvalues of a class of one-dimensional random non-Hermitian operators introduced recently by Hatano and Nelson. We prove that the eigenvalues are distributed along a curve in the complex plane. An equation for the curve is derived, and the density of complex eigenvalues is found in terms of spectral characteristics of a “reference” Hermitian disordered system. The generic properties of the eigenvalue distribution are discussed.Keywords
All Related Versions
This publication has 12 references indexed in Scilit:
- Almost Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre Eigenvalue StatisticsPhysical Review Letters, 1997
- Directed Quantum ChaosPhysical Review Letters, 1997
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering: Random matrix approach for systems with broken time-reversal invarianceJournal of Mathematical Physics, 1997
- Random matrix model approach to chiral symmetryNuclear Physics B - Proceedings Supplements, 1997
- Localization Transitions in Non-Hermitian Quantum MechanicsPhysical Review Letters, 1996
- Random Matrix Model of QCD at Finite Density and the Nature of the Quenched LimitPhysical Review Letters, 1996
- Statistics of S-matrix poles in few-channel chaotic scattering: Crossover from isolated to overlapping resonancesJETP Letters, 1996
- Passive Scalars, Random Flux, and Chiral Phase FluidsPhysical Review Letters, 1996
- Spectrum of Large Random Asymmetric MatricesPhysical Review Letters, 1988
- Circular LawTheory of Probability and Its Applications, 1985